Complex numbers
3.9What the syllabus asks of you
- understand the idea of a complex number, recall the meaning of the terms real part, imaginary part, modulus, argument, conjugate, and use the fact that two complex numbers are equal if and only if both real and imaginary parts are equal
- carry out operations of addition, subtraction, multiplication and division of two complex numbers expressed in Cartesian form x + iy
- use the result that, for a polynomial equation with real coefficients, any non-real roots occur in conjugate pairs
- represent complex numbers geometrically by means of an Argand diagram
- carry out operations of multiplication and division of two complex numbers expressed in polar form r(cos θ + i sin θ) ≡ re^(iθ)
- find the two square roots of a complex number
- understand in simple terms the geometrical effects of conjugating a complex number and of adding, subtracting, multiplying and dividing two complex numbers
- illustrate simple equations and inequalities involving complex numbers by means of loci in an Argand diagram
Read the notes first
Chapter 17: Complex numbers
Drill this topic
All 105 questions on Complex numbers, untimed — answer on paper, then mark yourself against the mark scheme.
Make a worksheet
Choose the years and how many questions, then print it with the answers on separate pages.
105 questions
These are structured questions, answered in working rather than by picking an option, so they are not listed here one by one. The drill above puts each in front of you with its mark scheme to check against.